Wold decomposition ($X_t=D_t+{\sum }_{j\ge 0}{c}_j{ϵ}_{t-j}$)

A second-order stationary time series decomposes into a deterministic component and a one-sided square-summable linear filter of a stationary time series of its mutually orthogonal linear innovations. Normalize $c_0=1$. For a causal invertible ARMA process with no deterministic component, the driving white noise is this innovation process: observations and innovations span the same closed past subspace, while the next innovation is orthogonal to it.